Psychology & Neuroscience ISSN: 1984-3054 [email protected] Pontifícia Universidade Católica do Rio de Janeiro Brasil

Valberg, Arne; Seim, Thorstein Neurophysiological correlates of color vision: a model Psychology & Neuroscience, vol. 6, núm. 2, 2013, pp. 213-218 Pontifícia Universidade Católica do Rio de Janeiro Rio de Janeiro, Brasil

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Neurophysiological correlates of color vision: a model Arne Valberg1 and Thorstein Seim2 1- Norwegian University of Science and Technology, Trondheim, ST, Norway 2- MikroSens, Slependen, AK, Norway

Abstract The tree-receptor theory of human color vision accounts for color matching. A bottom-up, non-linear model combining cone signals in six types of cone-opponent cells in the lateral geniculate nucleus (LGN) of primates describes the phenomenological dimensions hue, color strength, and lightness/brightness. Hue shifts with light intensity (the Bezold-Brücke phenomenon), and saturation (the Abney effect) are also accounted for by the opponent model. At the threshold level, sensitivities of the more sensitive primate cells correspond well with human psychophysical thresholds. Conventional Fourier analysis serves well in dealing with the discrimination data, but here we want to take a look at non-linearity, i.e., the neural correlates to perception of color phenomena for small and large fields that span several decades of relative light intensity. We are particularly interested in the mathematical description of spectral opponency, receptive fields, the balance of excitation and inhibition when stimulus size changes, and -to-LGN thresholds. Keywords: human color vision, opponent theory, three-color theory, three-receptor theory, perception, neuroscience.

Received 1 February 2012; received in revised form 2 July 2012; accepted 16 July 2012. Available online 18 November 2013.

Introduction and Russell De Valois (1965) in the U.S. started Current neuroscience has a good understanding of the recording the activity of single in the primate three-receptor theory of color vision, but the opponent- visual pathway. These recordings largely confirmed color theory (Hering, 1920) still lacks important neural the idea behind zone theories (e.g., Müller, 1930) and correlates. Even though one still searches for neural Schrödinger’s (1925) transformations, although it later processes that underlie the perception of the elementary became clear that some modifications were necessary. colors (yellow, blue, red, green, white and black), the Further quantitative data were gathered at the end of opponent color theory is as relevant as before. The the millennium in Otto Creutzfeldt and Barry B. Lee’s chromatic unique hues help us orient ourselves in laboratories at the Max Planck Institute for Biophysical color space more or less like four compass directions Chemistry in Göttingen, Germany. Around 1980, one of help orientation on the map. Scientific investigations us (A.V.) was invited to join this team. Our recordings imply that the elementary colors are associated with from opponent cells in the retina and lateral geniculate measurable physiological processes or states of the nucleus (LGN) of the macaque monkey (Macaca brain. How this comes about is unknown and poses fascicularis) led to a physiological model of color a fundamental philosophical question, e.g., how can vision that accounts for several color phenomena and a perceived quality like a certain color be related to a psychophysical data (Valberg et al., 1986a; Lee et al. physical-chemical state or process? Color qualities are 1987). different from such processes, and clarification of their In this paper we provide an overview of the model status within natural science must deal with the physical by listing its main features and their relation to the conditions for perception as well as thorough knowledge phenomenology and neurophysiology of color vision. of correlations between the qualitative properties and The main purpose is to point at some factors that need neural activity in the visual pathway. incorporation in this and all similar physiological By the 1960s, visual neuroscience had made great color vision models. In addition to spectral opponency, advances. Thorsten Wiesel and David Hubel (1966), relations that must be considered in a revised version are as follows:

Arne Valberg, Norwegian University of Science and • receptive fields and the response of opponent Technology, Section of Biophysics and Medical Technology, neurons to changing size of the stimulus N-7491 Trondheim, Norway. Thorstein Seim, MikroSens, • the excitatory/inhibitory balance within the Nedre Ås vei 63, N-1341 Slependen, Norway. Correspondence opponent receptive field that must be independent regarding this article should be directed to: Arne Valberg, of stimulus size (Seim et al., submitted) NTNU, Institute of Physics, N-7491 Trondheim, Norway. • the newly discovered (Seim et al., 2012) substantial Phone: +4773900754.E-mail: [email protected] threshold of the retinal input to an LGN 214 Valberg and Seim

A physiological model of color vision the Stockman-Sharpe cone fundamentals L, M and S Recent studies of color vision (see Shapley and (Stockman & Sharpe, 2000, generally accepted by CIE).

Hawken, 2011 for a review) have mainly dealt with The receptor hyperpolarization, VM, evoked by light can the properties of the neural channels that lead from be described by the hyperbolic Naka-Rushton formula the retina via the lateral geniculate nucleus to the of receptor excitations M: higher visual centers of the brain. Anatomical and n n n morphological studies have been complemented VM = M /(M + σ M) Eq. (1) with neurophysiological recordings, the latter often using system-theoretical methods like mathematical for the M-cone and similarly for responses VL and VS Fourier analysis of sensitivity and response (Lee et of the two other cone types. The exponent n is allowed al., 1990; Smith et al., 1992). Within this mechanistic to vary between 0.7 and 1.0 (Valeton & van Norren, framework the nerve cells are treated as filters of optical 1983). σ is the half-saturation constant (a parameter that information. Cells are characterized by their behavior to is interpreted as a sensitivity measure) with a different threshold contrasts and frequencies within the temporal value for each cone type. It was allowed to vary freely and spatial domains. This approach is, ideally, limited during simulation. This formula is sometimes called to linear systems. Therefore, in visual science such the Michaelis-Menton function but can also be traced analysis is adequate for neural activities at or near back to Archibald Hill (1910). The exponent n is often the threshold of visibility. It gives a rapid and useful called the Hill coefficient (Hsien-Che Lee, 2005). When overview of functional importance. This method is a plotted on a logarithmic luminance x-axis, this equation useful supplement but is perhaps less intuitive than more gives the characteristic sigmoid I-R curve for the cone traditional studies of neural correlates to perception of response. color phenomena that spans several decades of relative Let us use an ‘L-M’ opponent PC cell to illustrate the light intensity. Under normal conditions on a sunny simulation procedure. The cell receives its (prepotential) day, for a given adaptation, the activity of receptors input from a G. To model the firing and nerve cells must cope with at least five logarithmic rate NG of the retinal ganglion cell in imp/s, we use the units of intensity, that is a ratio of more than 1:100,000 equation between the lowest and the highest luminance, and non- linear behavior is the rule. NG = NL - NM, Eq. (2) Experiments have shown that psychophysical detection of color thresholds of humans, e.g., spectral where NL = ALVL and NM = AMVM and AL and AM are sensitivity to small spots projected upon a white amplitude scalars for the L and M cone contributions, background, corresponds well with the threshold respectively. The was adapted to a large achromatic sensitivity of the most sensitive opponent LGN cells field A that was shortly replaced by the test stimulus. of the macaque monkey (Lee et al., 1987). Also, The recorded ganglion cell input (the prepotential NP) the achromatic interval between detection and the was the difference between the response to the test field discrimination of hue corresponds nicely with the NG and the adaptation value NGA. The response is then: sensitivity difference of non-opponent magnocellular cells (MC cells) and of opponent cells (of either the NP = NG - NGA = NL - NM - N0, Eq. (3) parvocellular (PC cells) or the koniocellular types (KC cells) (Valberg and Lee, 1989). Moreover, at the where the L and M responses to the adaptation field suprathreshold level, the same size color differences are included in a single constant N0. The response of the and color scaling was found to correlate with relative ‘L-M’, LGN cell is then described by the equation firing rates in a network model combining six different types of opponent cells. The same applies to the change NLGN (L-M) = ALVL - AMVM - N0 Eq. (4) of hue with intensity (the Bezold-Brücke phenomenon) and saturation (the Abney effect) (Valberg et al., 1991). where AL and AM are amplitude weighting constants. In these experiments, large and small chromatic and In the early version of the model (Valberg et. al., 1987), achromatic stimuli of different relative intensities were N0 represented the anticipated activity of the LGN cell alternated with a 4 x 5 deg. white adaptation field of for zero luminance (when the adaptation field was constant luminance replaced by a black field). Later, due to the discovery of However, after the recent finding of a substantial a relatively high prepotential threshold spike frequency threshold in the afferent prepotential activity that elicits (a relative high frequency of the retinal ganglion cell a LGN response (particularly for small test fields; Seim response was required before the LGN cell started et al., 2012), improvements can be expected in the to fire, see Seim et al., 2012), it became necessary to modelling of LGN cell responses. Below we shall take give N0 the new interpretation that it represents the a closer look at the consequences of this new finding for anticipated activity of the prepotential (from the retinal the modelling approach. ganglion cell) for a zero luminance test field. In the

The first step is the excitation of cones by light optimization routine, N0 was therefore allowed to have absorption. For cone absorption spectra we use used a negative value relative to the LGN cell response. This Correlates of color vision 215

new role of N0 leads to improved response simulations shifted horizontally without changing their shape with values of n usually larger than 0.7. (Valberg et al., 1985). This is consistent with the half- The general version of Eq. (4) is given in Eq.(5) saturation constants σ in Eq. (1) being multiplied below with opponent combinations (differences) of by the same constant factor for both the L- and cone output signals, VS, VM and VL: M-cones. Increasing the test stimulus size to exceed that of the receptive field center usually reduced the

NLGN = ± ALVL ± AMVM ± ASVS - N0 Eq. (5) responsiveness (amplitude) of the LGN cell, but equally for excitatory and inhibitory processes. This attenuation For each cell, the optimization of the parameters in of the modelled I-R curve is achieved by reducing the

Eq.(5) was achieved by minimizing the root mean square amplitudes AL and AM by the same factor (see Eq. (2)). differences (rms) in firing rates between the measured responses in an I-R series and those predicted by the Interpretations model. Figure 1A shows an example of the simulation As a result of this extended and improved model, according to the “Pre-2010” version of the model (that new insight was gained as to the role of each cell type did not work well for small test field sizes as seen here in processing color information (Valberg & Seim, for the 699 nm stimulus (filled triangles)). Figure 1B 2008; Valberg, 2005). For instance, Increment (I cell) displays the much improved results when N0 is allowed and Decrement (D cell) cells (the ON- and OFF-types) to go negative (relative to the LGN cell response). can be shown to have opposite roles in discriminating graded luminance and chrominance (see Figure 2). Let us summarize: ‘L-M’ l-cell Pre-2010 model 200 180 • There are mainly four LGN parvocellular cone- 160 [imp/s] opponent cell types that combine L- and M-cones; a 140 N 120

- the ‘L-M’, I cells and the ‘L-M’, D cells, the ‘M-L,’

t 100 N 80 I cells and the ‘M-L’, D cells (Kaplan & Shapley, 60 40 1982). S-cones are connected to the ‘M (+L) –S’ N =0 20 0 cells and ‘S-L (+M)’ cells in the konicellular

Response 0 -20 pathway (Martin et al., 1997). 0.001 0.01 0.1 1 10 100 1000 • After an initial threshold, the firing frequency Luminance ratio Y of most opponent parvocellular LGN cell types to large fields can be mathematically simulated

‘L-M’ l-cell 0.33deg spot size by means of opponent inputs of excitatory and 200 inhibitory cone signals (proportional to receptor 150 potentials). [imp/s] a 100 • Whereas for a given adaptation, linearity between N - t 50 stimulus strength and response magnitudes applies N STT only over a relatively narrow stimulus range, non- 0 linear hyperbolic functions (Eq. (1)) work well for -50 N = -74 0 the cones over 5-6 logarithmic units of stimulus Response -100 intensity. 0.001 0.01 0.1 1 10 100 1000 • For opponent cells or a combination of opponent Luminance ratio Y cells, the firing rate in response to a chromatic Figure 1. (A) The data points show the recorded response stimulusrelative to that for a white stimulus of to a 0.33 deg stimulus for three wavelengths. The cell was the same luminancecorresponds to color strength a parvocellular (PC) LGN cell with ‘L-M’ opponency (filled or chroma (as, for instance, in the Munsell system). triangles: 699 nm; open squares 529 nm; filled circles: 500 • The magnitude of the responses (firing rates) of nm). The curves show the best simulation of the responses by these cells can be regarded as vector-lengths in an the “Pre-2010 model” using N = 0 imp/s, and the exponent n 0 opponent color diagram. = 0.7 in the response equation. The result is worse for the 699 nm stimulus. (B) Simulation of the same data as in (A) but • None of the color-space axes defined by the responses using the revised model described in the text, with a negative of these six cell types (see above) corresponds to the directions defined by the unique hues. N0 = -74 and an exponent n = 1.0. STT is a signal transfer threshold (of the prepotential firing) that must be reached by • A constant ratio of firing rates (responses) between the retinal input before the LGN cell starts to fire. The root cells with different opponencies corresponds mean square (rms) deviation between data and model is 2.5% closely to a perception of constant hue. This also of maximum response. accounts for the Abney effect (the change of hue with saturation). When the adaptation state of the cells was changed • As the luminance of a chromatic stimulus by projecting a steady white surround of different increases, the magnitude and ratio of firing rates luminance around the test spot, the I-R curves were of orthogonal opponent cells change as expected 216 Valberg and Seim

for the Bezold-Brücke phenomenon (when hue and human CIE luminous efficiency function V(λ) (Lee et chroma are combined) (Valberg et al., 1991). al., 1988). Because stimuli that have a luminance above • Brightness is well accounted for by the combined the magnocellular threshold, but below the chromatic responses of L/M, I cell types. Similarly, blackness threshold of PC and KC cells, have a colorless, (the opposite of lightness and brightness) is well achromatic appearance, it has been speculated that accounted for by the combined responses of L/M, magnocellular cells contribute to the surface perception D cell types (Figure 2; Valberg and Seim, 2008). of white (Hofer et al., 2005). However, their transient • The balance of cone inputs to an opponent cell firing of impulses speaks against such a possibility. is stable and does not change with test field size As indicated by the word “bistratified,” S-cone (Seim et al., 2012). activated cells have peculiar dendritic fields different from those of the midget ganglion cells. Their dendritic l-and D-cell response overlap field branches in two layers corresponding to theON

160 Sim E09U02 and OFF layers of other retinal cells (Dacey and Lee, LGN E09U02 1994). Until recently there were so few findings of cells 120 Sim E09U11 LGN E09U11 with excitatory L/M input combined with inhibitory [imp/s] a S-cone input that there were reasonable doubts that they N 80 -

t could play a role in color coding, but today this doubt N 40 has been removed (Valberg et al., 1986; Dacey and STT STT Packer, 2003; Tailby et al., 2008). Cells with excitatory 0 L/M cone input and inhibitory S-cone input discriminate Response -40 well between stimuli along a white-yellow dimension 0.001 0.01 0.1 1 10 100 in color space (but not in the white-blue direction), Luminance ratio Y contrary to PC-cells. Cells with an excitatory S-cone Figure 2. The distribution of information about light increments input discriminate well between blue and white stimuli. and light decrements on two opponent parvocellular cell types; the Increment and the Decrement cells (ON and OFF LGN and beyond cells). The signal transfer threshold STT is somewhat higher The discovery of a substantial prepotential threshold than -40 imp/s in both cases. As in Figure 1, only a model with spike frequency (the STT; Seim et al., 2012) has lead a high threshold value is able to account for the recorded data. to an improved simulation of LGN cell responses. This threshold leads to I-R curves that span a larger stimulus Comments range, resulting in a larger Hill coefficient, n, in Eq. Obviously, conscious perception of color qualities (1). The important fact that color vision is stable and arises neither in the photoreceptors nor in the opponent largely independent of stimulus size and adaptation cells of the retina and the LGN. However, constancy of finds its theoretical support in the simulations where several color percepts (such as a constant hue, constant the ratio of half saturation constants, σL/σM, and of the chroma (color strength), constant chromaticity, etc.) opponent response components, NL/NM, are independent seem to correlate with constancy in the relative responses of stimulus size and light level (Seim et al., 2012). of opponent neurons. Newton said that “the rays are The primate receptive and perceptive fields not coloured.” With due respect to Helmholtz, we must (Spillmann, 1971) associated with the dendritic fields add that “colours neither reside in the receptors nor in of opponent cells are still discussed. The current debate the cone-opponent cells of the retina and LGN” (see is concerned with the organization of cone opponency Valberg, 2001). However, the same perceptual attribute in simple concentric and double opponent cells. For the (as, for example, a certain orange hue independent retina and LGN, the classical view is one of a center of purity) seems to correlate with a constant ratio of and surround organization that for I-center cells form response magnitudes between cone-opponent neurons. a “Mexican hat” spatial sensitivity profile with an Constant color strength (chroma) in an equiluminous excitatory cone type in the center and another inhibitory chrominance diagram correlates well with a constant cone type in the surrounding annulus. This spatial vector length from the white point in a vector space sensitivity profile has commonly been modelled asa based on neural responses. Difference of Gaussian (DoG) function. However, due PC- and KC-cone opponent channels have important to some inconsistencies in the DoG modelling of the roles in color vision, whereas the retinal parasol cells response of an opponent cell as a function of stimulus that projects to the LGN magnocellular cells, sum L- size, it appears that power functions would be better and M-cone inputs and do not contribute directly to (Seim et al. 2011; 2012). The relative size of center and color vision. Their second harmonic |L-M| rectified surround seems to vary among cell types, and cells with opponent response correlates with border distinctness S-cone inputs seem to have coextensive or overlapping between equiluminant chromatic stimuli (Valberg et al., excitatory and inhibitory receptive fields. Higher 1992). These transiently responding magnocellular cells up, in area V1 of the brain, one frequently finds so- have an unusually high luminance contrast sensitivity called double opponent receptive fields with one cone and a spectral sensitivity that corresponds closely to the opponency in the center (e.g., L–M) and the opposite Correlates of color vision 217

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